# Towards holography in the BV-BFV setting

## TL;DR

This paper explores how the BV-BFV formalism can naturally address descent equations and facilitate holographic dualities, demonstrating a correspondence between bulk gauge theories and boundary theories through AKSZ constructions.

## Contribution

It introduces a novel approach linking BV-BFV formalism with holography and reproduces known correspondences like Chern-Simons/WZW via AKSZ methods, extending to BF theory.

## Key findings

- Reproduces Chern-Simons to WZW correspondence using AKSZ construction.
- Shows how BV-BFV formalism naturally solves descent equations.
- Proposes a semi-classical interpretation of the quantum holographic principle.

## Abstract

We show how the BV-BFV formalism provides natural solutions to descent equations, and discuss how it relates to the emergence of holographic counterparts of given gauge theories. Furthermore, by means of an AKSZ-type construction we reproduce the Chern-Simons to Wess-Zumino-Witten correspondence from infinitesimal local data, and show an analogous correspondence for BF theory. We discuss how holographic correspondences relate to choices of polarisation relevant for quantisation, proposing a semi-classical interpretation of the quantum holographic principle.